Related papers: Two-parametric fractional statistics models for an…
For three anyons confined in a harmonic oscillator, only the class of states that interpolate nonlinearly with the statistical parameter contributes to the third virial coefficient of a free anyon gas. Rather than evaluating the full…
The main object of Bayesian statistical inference is the determination of posterior distributions. Sometimes these laws are given for quantities devoid of empirical value. This serious drawback vanishes when one confines oneself to…
In many applications, the variables that characterize a stochastic system are measured along a second dimension, such as time. This results in multivariate functional data and the interest is in describing the statistical dependences among…
This article explores a general factor structure for high-dimensional nonstationary functional time series, encompassing a wide range of factor models studied in the existing literature. We investigate the asymptotic spectral behaviors of…
We comment on the significance of the results in the paper by Nakamura et al (2020). The experimental result measures the phase for a repeated elementary exchange of two identical quasiparticles, and shows that the quasiparticles are…
Change point tests for abrupt changes in the mean of functional data, i.e., random elements in infinite-dimensional Hilbert spaces, are either based on dimension reduction techniques, e.g., based on principal components, or directly based…
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied…
Anyons - particles carrying fractional statistics that interpolate between bosons and fermions - have been conjectured to exist in low dimensional systems. In the context of the fractional quantum Hall effect (FQHE), quasi-particles made of…
This paper provides a semiparametric model of estimating states of the volatility defined as the squared diffusion coefficient of a stochastic differential equation. Without assuming any functional form of the volatility function, we…
The potential of location-shift models to find adequate models between the proportional odds model and the non-proportional odds model is investigated. It is demonstrated that these models are very useful in ordinal modeling. While…
Fundamental rules and definitions of Fractional Differintegrals are outlined. Factorizing 1-D and 2-D Helmholtz equations four fractional eigenfunctions are determined. The functions exhibit incident and reflected plane waves as well as…
The theory of fractional calculus in the complex plane was not built with a specific application in mind. The main obstacle to application was the difficulty with obtaining analytic continuations of fractional derivatives and integrals. It…
Statistical dependence between hypotheses poses a significant challenge to the stability of large scale multiple hypotheses testing. Ignoring it often results in an unacceptably large spread in the false positive proportion even though the…
This paper investigates the problem of online statistical inference of model parameters in stochastic optimization problems via the Kiefer-Wolfowitz algorithm with random search directions. We first present the asymptotic distribution for…
In certain situations, such as one-particle inclusive processes, it is possible to model the hadronization through Fragmentation Functions (FFs), which are universal non-perturbative functions extracted from experimental data through…
We provide a comprehensive set of new results on the impact of mis-specifying the short run dynamics in fractionally integrated processes. We show that four alternative parametric estimators - frequency domain maximum likelihood, Whittle,…
The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable L\'evy processes, and fractional Brownian motion. For this reason it may be regarded as a basic building block for continuous time…
Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of n-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk and…
We examine two stochastic processes with random parameters, which in their basic versions (i.e., when the parameters are fixed) are Gaussian and display long range dependence and anomalous diffusion behavior, characterized by the Hurst…
Functional factor analysis is an important dimension reduction method for functional and longitudinal data. Factor loadings give insight into patterns of variability of the observations, while latent factors provide a low-dimensional…